Because he has nowhere else to go, the Doctor stays.
Reinette uses her charms (and, he suspects, other things) to get him employed as King's Physician, telling him that he might as well be a doctor if he is to stay here. It annoys him to be at someone else's beck and call, and his deference is weak enough that it is only covered for by the fact that his medical knowledge is far in advance of everyone else's.
He has a room full of clockwork apparatus, technology salvaged from the stranded service droids and the few useful bits and pieces he had in his pockets when he came through the looking-glass. It is not enough.
The rift in Cardiff is still open. There is a similar tear near Lilongwe and another in Hangzhou. All of them must stay open so that he can close them in his own past at a later date. He has no memory of encountering himself here, and there is no Gallifrey to summon. If he had thought, he would have set the recall on the TARDIS, but he did not think and now he is not sure if there are enough thoughts in his head to help him.
He has his mind, some inadequate Enlightenment science, and all the time in the world.
And he has Reinette.
He wants to take her places, and cannot.
He tells her of Gallifrey, fills in details of the images she saw in his mind. She asks about a woman who looked like her, and he is honest and not evasive (though certain details are his own to keep). He tells her things because she already knows them, because she already understands. He listens to stories about her life, knowing them already and hanging on her every word.
They speak to people who know a great deal about the too-little science in this time. Jean D’Alembert and Leonhard Euler are invited to Versaille to see a marvellous and mysterious contraption, asked for any thoughts on how certain things might be made to work with current technology.
The Doctor promises to show Reinette the stars, knowing it is a foolish thing to say and meaning it anyway.
"How long will it be before you grow tired of me?" she asks.
"I don't know. How many more sexual positions can you think of?"
She does not laugh. "You always leave. I saw that in your mind. And you left your friends when you came to me."
"Time travel. I can be back before they've even missed me. Both of us," he adds, and twines his fingers with hers.
She is a well-trained courtesan, and does not ask the question he can see in her eyes. If you had to choose, they ask, which would it be? He wants to tell her that she should speak her mind, that she should stop thinking of herself as someone's mistress. But then he would have to answer her question.
"She loves you," says Louis, recovered from a brief fever and grateful enough to hide his anger.
"She loves you as well," he says, because it is true, even if the degree of feeling is obviously different even to him.
"And I love her," says the monarch, "and thought that a king could have any woman he wanted." He raises a glass in a mocking salute. "I had not reckoned on angels."
"I'm not an angel," says the Doctor, carefully but perhaps not careful enough.
"Then you would do well to act like one. Be sure to remember that she is my woman, not yours."
The Doctor thinks that Reinette is her own woman, but keeps the opinion to himself. He is no longer free to do as he pleases.
He spends too much time in her rooms, sometimes staring at the fireplace that brought him to her and later failed to free him, sometimes watching nothing but her. They speak in hushed voices, exchange private jokes that no one else would understand, play chess and make love.
He neglects his attempts to return to the future, occasionally forgets that he has no wish to remain here. If he wastes time it does not matter, because he has plenty.
Various women court him, and for a month he is engaged to one of them simply to stop everyone pestering him. He should be married, says Reinette, lest people talk. He has known a loveless match before, so long ago, and this would be no different.
He remains unwed, because his pragmatism is already stretched thin, and love is one of the few things he has left. He has no family for anyone to marry into, and his position at the court is tenuous at best. He is openly spoken of as the foreign lover of the King's mistress, and just because there was no such scandal does not mean that there will not be. Time is in flux, even as he is forced to live his days in sequence and to hold back on his natural instinct for chaos.
Every time he is forced to live on Earth (once because of the Time Lords, and now because there are none) he works for a regime he might have toppled. He suspects there is an irony in that, and wonders if there is such a thing as fate.
They get careless. He forgets that he has no means of escape and is confronted by an angry Louis XV after forgetting that he must sleep in his own bed.
"You saved my life," he is told. "Many times, and for that I am grateful. But if I discover you in her bed again, I will find a way to kill an angel."
The Doctor and Reinette leave Versailles that afternoon, giddy.
They travel to England, because the Doctor needs electricity and Benjamin Franklin has some experience in the matter and is in the area. Alessandro Volta is only fourteen years old and modern batteries will not provide enough current. The Doctor needs someone clever enough to help and famous enough not to go public and rename voltage.
He agrees to meet Ben in America if he is still around and stranded. He catches Reinette's expression and amends it to "we," ignoring the knowledge that surely by then he will have buried her.
He has always entertained a fantasy of domestic life. It is a set of notions that is overly romantic and at the same time mundane and uninteresting. It appeals less when he has no alternative, but the reality is magical in its own way.
He is still lonely, but it hurts less.
Because he is not native to this century, it takes him far too long to realise that Reinette expects him to marry her. He wonders why she did not just ask outright.
"I don't have anything to give you," he says, "not even a name."
"I already have a name," she returns, because she has become something of an anchronism herself.
"You do," he agrees, and kisses her shoulder. "I doubt a church would even let us through the door, though."
"We are always in the sight of God," she says. "He does not reside only in churches."
She looks so solemn that he cannot stop himself from joking. "Can you keep me in the style to which I am accustomed?"
"If you swear not to take another woman to our bed."
"Unless you're there as well," he agrees. "What about a man?"
"Only in my company."
"Of course. Anything else?"
She knows better than to ask for things she knows he cannot give her, and shakes her head.
"Then I now pronounce us husband and wife. Can I kiss the bride?"
She nods, and he does.
They have one child, who is weak from the ill-formed hearts in her chest and born before anyone could heal them. She has few days and they tick away quickly.
He has lost too many children, and his eyes sting as he leads Reinette from their daughter's grave.
They meet George III towards the end of the Seven Years War, and the Doctor writes a sarcastic article in The North Briton because the king has insulted his wife. It will prove prescient in the years to come, and for now is enough to make the couple the darlings of John Wilkes and the more radical Whigs. When Wilkes is forced to flee to Paris, he takes letters for Reinette's family and an apology from the two that might make its way to Versailles.
It is not the worst century to be trapped in. The Doctor takes Reinette to Edinburgh and they dance among the stars of the Enlightenment. The Euro-American world edges closer to revolution as they move, always slightly out of time with the music.
He knows that events will test his resolve, but at least he will not have to live through the 1979 General Election again.
He does not look for Sabbath, but he begins to understand how that man knew so much about him. They are both in the orbit of the Hellfire Club, because sufficiently advanced technology is indistinguishable from magic. It will take longer to return without the help of a man who could certainly assist them, but the Doctor has learned something like patience.
"He stole my heart," he tells Reinette. "I mean literally. I wasn't in love with him or anything. I had a spare, obviously, but it was quite painful."
"It always is," she whispers, and he notices once more how many lines have appeared on her skin in the years they have been together.
She does not die when she is supposed to, outlives the illness that should have taken her. He tells himself that plenty of people have lived because of him, just as far too many have died under his influence.
He waits for the Reapers, and they never come.
They spend a futile year searching for the Comte de Saint-Germain, who seems to flit through time as the Doctor once did.
They find that the man is mere charlatan. When questioned his answers are wrong and he knows nothing that he shouldn't. He is skilled at chemistry and the arts, but his talents are entirely Earthly.
"I had heard the same of you," says Saint-Germain when the Doctor calls him a liar. "They still speak of you at Versailles. The angel who stole a woman from a king. I admit I am impressed. You must tell me how you did it."
"I didn't steal her," sighs the Doctor, words he has repeated uncountable times.
"Then perhaps she stole you. Plucked an angel from the heavens and tempted him to sin. You hold onto that woman as though she were the only thing that binds you to this world. Is she?"
"No," says the Doctor, and perhaps he is a liar as well.
Because it amuses him, he finds a Tarot deck and a woman who claims second sight. A foolish whim for a man who does not believe in literal magic, but inevitable for one who is used to knowing the future.
"I used to do this sort of thing," says the Doctor as Reinette shuffles her cards, smiling. "Not with cards, but my method was fairly accurate."
"What did you use?" asks the woman.
"A blue box," he grins. "Bit esoteric and not all that reliable, but it worked. I'm hoping to start doing readings again sometime soon. House calls, that sort of thing."
Reinette's cards are laid on the table, and the fortune-teller examines them for a moment, skin growing pale and eyes fixed open.
"You should not be living," says the woman, and refuses any payment.
Back in England they meet Tom Paine, who says, "The world is changing."
"Debout, les damnés de la terre," says the Doctor. "Le monde va changer de base." It is 1766 and Reinette's world is already fading. She can exist only in a brief historical moment, and even in plainer clothes than she ever wore in France she is still a product of the ancien régime. She is not timeless, however much the Doctor likes to pretend that she is -- there are certain truths that even he can't deny.
But the world is changing, in ways that will bring joy as well as sorrow. The advancing Industrial Revolution takes the Doctor one step closer to the future with every day that passes, and perhaps he will have time to show his love the stars he promised her so many years ago.
"I like you," the Doctor says, tapping his new friend on the arm, "you've got a lot of common sense in you."
She dies three years too late. He hopes it will not make a difference, and does not care that it might.
"Let me go this time," she whispers, when he tries to make her stay.
"No," he says, because he can heal her, because he does not let things happen as they should. He is the Doctor; he is endless; he is lonely; he is in love.
"You can't keep me forever," she tells him. "I have to leave eventually. Let me choose my own time."
"It doesn't have to be now. I can cure you. You could have years."
"I've done so many things," she breathes, "more than enough for one lifetime."
He protests. "There's so much more you could still do."
"I was a king's mistress and the lover of an angel," she smiles, "isn't that enough?"
"Oh, you're so much more than that."
"Then let me be my own woman."
"Everything ends, Doctor."
And she is right.
He finally fits his clockwork devices together, and they slot into a whole so easily that he wonders why the task seemed so difficult before. In no time at all (and many centuries later) his signal is received and he is rescued by a man who has not yet met him and will not remember this when they meet again in London, 1941. His saviour will not remember that they kissed, and the Doctor will be years and a body away from the gratitude that makes his lips impulsive.
He returns to the ship alone, because he has damaged time enough. Rose clings to him with red eyes and says that they have waited an hour. "It felt like forever," she tells him.
"Oh, ye of little faith," he says, breaking the embrace in case he gives too much away. He pokes Mickey in the chest. "You I'd expect it from," he jokes, and keeps smiling even as he realises that he is still forming his words in French.
"How long were you stuck there?" asks Rose, concern and not a little envy written on her face.
"Not long," he says. "Hardly any time at all."